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CFA Level I · Study Guide

Derivatives

5-8% of exam10 modulesDemanding
Overview

Derivatives covers forward contracts, futures, swaps, and options — their pricing, payoffs, and uses in risk management. At Level I the emphasis is on understanding no-arbitrage pricing principles and the payoff profiles for each instrument. The Black-Scholes-Merton (BSM) model inputs and put-call parity are frequently tested. Derivatives account for 5–8% of the exam and rewards candidates who understand the conceptual logic of pricing.

Key Formulas

The formulas that appear most often

Forward Price (no-dividend asset)
F₀ = S₀ × (1 + r)^T
Continuous compounding: F₀ = S₀ × e^(rT); cost of carry model — forward = spot × growth factor
Forward Price (dividend-paying asset)
F₀ = (S₀ − PV(D)) × (1 + r)^T
PV(D) = present value of dividends paid during the forward period
Put-Call Parity
C + PV(X) = P + S₀
C = call price; P = put price; X = strike; S₀ = spot; reranged: C − P = S₀ − PV(X)
Call Option Payoff at Expiration
Payoff = max(0, S_T − X)
Profit = Payoff − call premium paid (× (1+r)^T)
Put Option Payoff at Expiration
Payoff = max(0, X − S_T)
BSM — Option Greeks (directional)
Delta (Δ): ∂C/∂S; Gamma (Γ): ∂²C/∂S²; Vega: ∂C/∂σ; Theta (Θ): ∂C/∂t; Rho (ρ): ∂C/∂r
Call delta ∈ (0,1); put delta ∈ (−1,0); gamma peaks ATM; vega positive for both calls and puts
Interest Rate Swap — Net Payment
Net Payment = (Fixed Rate − Floating Rate) × Notional × Days/360
Fixed-rate payer benefits when floating rates rise; floating-rate payer benefits when rates fall
High-Yield Exam Areas

What actually gets tested

1

No-arbitrage pricing: the forward price is the price that makes the present value of entering the contract equal to zero. Any price above or below allows riskless profit — the exam tests whether you can identify and exploit the arbitrage.

2

Option moneyness: in-the-money (intrinsic value > 0), at-the-money (intrinsic value = 0), out-of-the-money (intrinsic value = 0). Only ITM options have intrinsic value; time value exists for all options before expiration.

3

BSM inputs and sensitivities: option value increases with stock price (call), time to expiration (usually), volatility (both), and risk-free rate (call). Call and put values move in opposite directions with respect to underlying price and risk-free rate.

4

Swaps as a series of forwards: a fixed-for-floating interest rate swap can be replicated as a portfolio of forward rate agreements (FRAs). The swap rate is the fixed rate that makes the swap's NPV equal to zero at initiation.

Common Mistakes

Where candidates lose marks

✕

Confusing the forward price (the contracted delivery price) with the value of the forward contract (which starts at zero and changes over time as market prices move).

✕

Getting put-call parity wrong under different scenarios — memorise the relationship C + PV(X) = P + S₀ and practice rearranging it to isolate each variable.

✕

Forgetting that options can only be exercised at expiration for European options, while American options can be exercised any time. American calls on non-dividend-paying stocks are never optimally exercised early.

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